LIE IDEAL AND GENERALIZED JORDAN REVERSE DERIVATIONS ON SEMIPRIME RINGS

2017 ◽  
Vol 102 (12) ◽  
pp. 3093-3106
Author(s):  
C. Jaya Subba Reddy ◽  
A. Sivakameshwara Kumar ◽  
B. Ramoorthy Reddy
Keyword(s):  
Lie Ideal ◽  
Semiprime Rings

scholarly journals Generalized Derivations on Power Values of Lie Ideals in Prime and Semiprime Rings

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Vincenzo De Filippis ◽  
Nadeem UR Rehman ◽  
Abu Zaid Ansari
Keyword(s):  
Lie Ideal ◽  
Generalized Derivations ◽  
Fixed Integer ◽  
Free Ring ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Positive Integers ◽  
Torsion Free

LetRbe a 2-torsion free ring and letLbe a noncentral Lie ideal ofR, and letF:R→RandG:R→Rbe two generalized derivations ofR. We will analyse the structure ofRin the following cases: (a)Ris prime andF(um)=G(un)for allu∈Land fixed positive integersm≠n; (b)Ris prime andF((upvq)m)=G((vrus)n)for allu,v∈Land fixed integersm,n,p,q,r,s≥1; (c)Ris semiprime andF((uv)n)=G((vu)n)for allu,v∈[R,R]and fixed integern≥1; and (d)Ris semiprime andF((uv)n)=G((vu)n)for allu,v∈Rand fixed integern≥1.

scholarly journals (U. M)-derivations in completely semiprime ?-rings

2016 ◽  
Vol 51 (1) ◽  
pp. 69-74
Author(s):  
MM Rahman ◽  
AC Paul
Keyword(s):  
Semiprime Ring ◽  
Subject Classification ◽  
Lie Ideal ◽  
Semiprime Rings ◽  
And Mathematics

The objective of this paper is to extend and generalize some results of (Rahman and Paul, 2014) in completely semiprime ?- rings. We prove that, if is an admissible Lie ideal of a completely semiprime ?-ring and d is a (U, M) -derivation of then d(u?v)=d(u)?v+u?d(v) for all u, v ? U and ? ? ?Mathematics Subject Classification: 13N15, 16W10, 17C50Bangladesh J. Sci. Ind. Res. 51(1). 69-74, 2016

Generalized derivations preserving Engel condition in prime and semiprime rings

2020 ◽  
pp. 2150041
Author(s):  
Rita Prestigiacomo
Keyword(s):  
Prime Ring ◽  
Algebraic Closure ◽  
Quotient Ring ◽  
Lie Ideal ◽  
Extended Centroid ◽  
Generalized Derivations ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings ◽  
Martindale Quotient Ring ◽  
Engel Condition

Let [Formula: see text] be a prime ring with [Formula: see text], [Formula: see text] a non-central Lie ideal of [Formula: see text], [Formula: see text] its Martindale quotient ring and [Formula: see text] its extended centroid. Let [Formula: see text] and [Formula: see text] be nonzero generalized derivations on [Formula: see text] such that [Formula: see text] Then there exists [Formula: see text] such that [Formula: see text] and [Formula: see text], for any [Formula: see text], unless [Formula: see text], where [Formula: see text] is the algebraic closure of [Formula: see text].

On Certain Identities with Automorphisms on Lie Ideals in Prime and Semiprime Rings

2019 ◽  
Vol 26 (01) ◽  
pp. 93-104
Author(s):  
Vincenzo De Filippis ◽  
Nadeem ur Rehman
Keyword(s):  
Prime Ring ◽  
Lie Ideal ◽  
Standard Identity ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings

Let R be a prime ring of characteristic different from 2, Z(R) its center, L a Lie ideal of R, and m, n, s, t ≥ 1 fixed integers with t ≤ m + n + s. Suppose that α is a non-trivial automorphism of R and let Φ(x, y) = [x, y]t – [x, y]m [α([x, y]),[x, y]]n [x, y]s. Thus, (a) if Φ(u, v) = 0 for any u, v ∈ L, then L ⊆ Z(R); (b) if Φ(u, v) ∈ Z(R) for any u, v ∈ L, then either L ⊆ Z(R) or R satisfies s4, the standard identity of degree 4. We also extend the results to semiprime rings.

A study of derivable mappings of semiprime rings

2018 ◽  
Vol 7 (1-2) ◽  
pp. 19-26
Author(s):  
Gurninder S. Sandhu ◽  
Deepak Kumara
Keyword(s):  
Associative Ring ◽  
Semiprime Ring ◽  
Nonzero Ideal ◽  
Lie Ideal ◽  
Commutativity Theorems ◽  
Semiprime Rings

Throughout this note, \(R\) denotes an associative ring and \(C(R)\) be the center of \(R\). In this paper, it isproved that a non-central Lie ideal \(L\) of a semiprime ring \(R\) contains a nonzero ideal of \(R\) and this result isused to obtain several commutativity theorems of \(R\) involving multiplicative derivations. Moreover, someresults on one-sided ideals of \(R\) are given.

scholarly journals Notes on the higher derivations on prime rings

2018 ◽  
Vol 37 (4) ◽  
pp. 61-68 ◽  
Author(s):  
Mehsin Jabel Atteya
Keyword(s):  
Lie Ideal ◽  
Prime Rings ◽  
Semiprime Rings ◽  
Higher Derivation

The main purpose of thess notes investigated some certain properties and relation between higher derivation (HD,for short) and Lie ideal of semiprime rings and prime rings,we gave some results about that.

scholarly journals Derivations on Lie ideals of completely semiprime ? -rings

2016 ◽  
Vol 27 (1) ◽  
pp. 51-61
Author(s):  
MM Rahman ◽  
AC Paul
Keyword(s):  
Semiprime Ring ◽  
Jordan Derivation ◽  
Lie Ideal ◽  
Semiprime Rings ◽  
Torsion Free

The aim of the paper is to prove the following theorem concerning a class of ? -rings. LetM be a 2-torsion free completely semiprime ? -ring satisfying the condition a?b?c = a?b?c, for all a,b,c?M and ? ,? ?? ; U be an admissible Lie ideal ofM . If d :M ?M is a Jordan derivation on U of M , then d is a derivation on U of M .Bangladesh J. Sci. Res. 27(1): 51-61, June-2014

scholarly journals On Skew Left n-Derivations with Lie Ideal Structure

2019 ◽  
Vol 16 (2) ◽  
pp. 0389
Author(s):  
Faraj Et al.
Keyword(s):  
Ideal Structure ◽  
Lie Ideal ◽  
Prime And Semiprime Rings ◽  
Semiprime Rings

In this paper the centralizing and commuting concerning skew left -derivations and skew left -derivations associated with antiautomorphism on prime and semiprime rings were studied and  the commutativity of Lie ideal under certain conditions were proved.

On Jordan Structure in Semiprime Rings

1976 ◽  
Vol 28 (5) ◽  
pp. 1067-1072 ◽  
Author(s):  
Ram Awtar
Keyword(s):  
Semiprime Ring ◽  
Nonzero Ideal ◽  
Lie Ideal ◽  
Additive Subgroup ◽  
Jordan Structure ◽  
Semiprime Rings

A remarkable theorem of Herstein [1, Theorem 2] of which we have made several uses states: If R is a semiprime ring of characteristic different from 2 and if U is both a Lie ideal and a subring of R then either U ⊂ Z (the centre of R) or U contains a nonzero ideal of R. In a recent paper [3] Herstein extends the above mentioned result significantly and has proved that if R is a semiprime ring of characteristic different from 2 and V is an additive subgroup of R such that [V, U] ⊂ V, where U is a Lie ideal of R, then either [V, U] = 0 or V ⊃ [M, R] ≠ 0 where M is an ideal of R. In this paper our object is to prove the following.

scholarly journals Jordan Derivations on Lie Ideals of Semiprime ?-Rings

2016 ◽  
Vol 34 ◽  
pp. 35-46
Author(s):  
Md Mizanor Rahman ◽  
Akhil Chandra Paul
Keyword(s):  
Additive Mapping ◽  
Jordan Derivation ◽  
Lie Ideal ◽  
Semiprime Rings ◽  
Torsion Free

Let M be a 2-torsion free semiprime G-ring satisfying the condition a?b?c = a?b?c,?a, b, c ?M and ?, ? ??. Let U be an admissible Lie ideal of M that is, u?u ? U,?u ? U, ? ?G and U ?Z(M), the centre of M. If d : M -> M is an additive mapping such that d is a Jordan derivation on U of M, then d is a derivation on U.GANIT J. Bangladesh Math. Soc.Vol. 34 (2014) 35-46

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